Thutmose was the birth name of four different rulers of the New Kingdom's 18th dynasty. The name of the god Thoth is an ancient Greek transcription of the original ancient Egyptian name Djehuty. Hence the original name would have sounded closer to "Djehutimes".
This block of painted limestone is from the temple of Thutmose III from Deir El Bahari, and originally was part of the temple wall. This is exhibited today in the Luxor Museum.
We can see 3 cartouches, one partial and two in full, all coloured with a yellowish-brown background. A cartouche is an oval with a line at one ending indicating that the text enclosed is a royal name. Cartouches are first noted during the third dynasty of the Old Kingdom. The word cartouche is of French origin, the ancient Egyptian name is "shenu".
The partial one (last one from left) shows the hieroglyphs "kheper" and "ka" - the scarab beetle and the upheld arms - part of the throne name of Thutmose I - Aa kheper ka Ra, which means "Great is the manifestation of the soul of Ra".
The two full cartouches show the throne name (first cartouche from left) and birth name - or also called the Son of Ra name - (second cartouche from left) of Thutmose III: "Men kheper Ra", meaning "Lasting is the Manifestation of Ra" and "Djehutimes (nefer) kheper", meaning "Thoth is born, beautiful of form".
You will notice that one of the signs have been chiseled out (?) and I am making the assumption that this was the sign "nefer". Another variant of Thutmose III's birth name was "Djehutimes sema kheper" or "Thoth is born, united of manifestations". That name uses the sign "sema", which is also a single sign, but it's shape is different and my personal guess is that the sign used in this particular cartouche was nefer rather than sema.
Have a look at the two different names below - which one do you think rather resembles the one with the missing sign?